Non-positive Components Research Articles

Event-triggered control of positive switched systems with randomly occurring state saturation

This paper is concerned with the event-triggered control of positive switched systems with randomly occurring state saturation. First, a vector-based event-triggering condition is established. Thus, interval and polytope approaches are used to deal with the positivity and stability of the systems and the saturation, respectively. An event-triggered controller and the corresponding domain of attraction are designed by decomposing gain matrix into the sum of non-negative and non-positive components. The proposed design approach is developed for the systems with input saturation. Finally, two examples are given to illustrate the effectiveness of the proposed design.

Dual-channel event-triggered control for positive nonlinear systems

This paper focuses on the problem of dual-channel event-triggered control for positive nonlinear systems. A dual-channel event-triggered transmission scheme is proposed to determine whether the data packets should be released or not. Two 1-norm-based event-trigger conditions are designed for the sensor-controller channel and controller-actuator channel, respectively. The condition of the system remaining positivity with the designed event-trigger conditions and feedback control law is provided. By using the Lyapunov method and matrix decomposition technique, a sufficient criterion ensuring the closed loop system to be asymptotically stable is proposed. For the linearisation purpose, the control gain is delicately decomposed into a nonnegative component and a non-positive component. Zeno behaviour of the designed event-triggered transmission of sampled data packets is further rigorously proved to be excluded. An example of water pollution control system is provided to show the effectiveness of the obtained results.

Event-Triggered L1-Gain Control of Nonlinear Positive Switched Systems

This paper is concerned with the event-triggered L1-gain control of a class of nonlinear positive switched systems. First, an event-triggering condition in the form of 1-norm is presented for the systems. By virtue of the event-triggering strategy, the original system is transformed into an interval uncertain system. An event-triggered L1-gain controller is designed by decomposing the controller gain matrix into the sum of nonnegative and non-positive components. Under the design controller, the resulting closed-loop systems are positive and L1-gain stable. The obtained approach is developed for the systems subject to input saturation. All presented conditions are solvable in terms of linear programming. Finally, two examples are provided to verify the effectiveness of the design.

Reliable control for positive switched systems with random nonlinearities

This paper proposes a reliable control of positive switched systems with random nonlinearities which may induce the security problem of the systems. The random nonlinearities are governed by stochastic variables obeying the Bernoulli distribution. A switched linear copositive Lyapunov function is employed for the systems. Using a matrix decomposition approach, the gain matrix of controller is formulated by the sum of nonnegative and non-positive components. A reliable controller is designed for positive switched systems with actuator faults by virtue of linear programming. Under the designed reliable controller, the systems can resist some possible security risks triggered by random nonlinearities and actuator faults. The obtained approach is developed for systems subject to exogenous disturbances. Finally, two examples are provided to verify the validity of the obtained results.

Distributed model predictive control of positive Markov jump systems

This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS

We present a model and propose an approach to compute an ap- proximate solution of Fully Fuzzy Linear System (FFLS) of equations in which all the components of the coecient matrix are either nonnegative or nonpos- itive. First, in discussing an FFLS with a nonnegative coecient matrix, we consider an equivalent FFLS by using an appropriate permutation to simplify fuzzy multiplications. To solve the m n permutated system, we convert it to three m n real linear systems, one being concerned with the cores and the other two being related to the left and right spreads. To decide whether the core system is consistent or not, we use the modied Huang algorithm of the class of ABS methods. If the core system is inconsistent, an appropri- ate unconstrained least squares problem is solved for an approximate solution. The sign of each component of the solution is decided by the sign of its core. Also, to know whether the left and right spread systems are consistent or not, we apply the modied Huang algorithm again. Appropriate constrained least squares problems are solved, when the spread systems are inconsistent or do not satisfy fuzziness conditions. Then, we consider the FFLS with a mixed single-signed coecient matrix, in which each component of the coecient matrix is either nonnegative or nonpositive. In this case, we break the m n coecient matrix up to two m n matrices, one having only nonnegative and the other having only nonpositive components, such that their sum yields the original coecient matrix. Using the distributive law, we convert each

Production Frontiers and Panel Data

This article considers estimation of a stochastic frontier production function-the type introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). Such a production frontier model consists of a production function of the usual regression type but with an error term equal to the sum of two parts. The first part is typically assumed to be normally distributed and represents the usual statistical noise, such as luck, weather, machine breakdown, and other events beyond the control of the firm. The second part is nonpositive and represents technical inefficiencythat is, failure to produce maximal output, given the set of inputs used. Realized output is bounded from above by a frontier that includes the deterministic part of the regression, plus the part of the error representing noise; so the frontier is stochastic. There also exist socalled deterministic frontier models, whose error term contains only the nonpositive component, but we will not consider them here (e.g., see Greene 1980). Frontier models arise naturally in the problem of efficiency measurement, since one needs a bound on output to measure efficiency. A good survey of such production functions and their relationship to the measurement of productive efficiency was given by F0rsund, Lovell, and Schmidt (1980).

A Monte Carlo study of estimators of stochastic frontier production functions

1. Introduction In recent papers which appeared almost simultaneously, Aigner, Love11 and Schmidt (ALS) (1977) and Meeusen and van den Broeck (1977) proposed a new error specification for frontier production function models. The specification is that the error term is the sum of two components ~ one normal with zero mean, and the other non-positive. ALS refer to a model with this error specification as a ‘stochastic frontier’, since the non-positive component of the disturbance represents the shortfall of actual output from the frontier, while the frontier contains the normal component of the disturbance, and is therefore stochastic. This specification avoids the serious statistical difficulties [discussed by Schmidt (1976) and Greene (1980)] which are encountered in the estimation of full frontiers - that is, in the presence of a purely non-positive error term. Any number of one-sided distributions exist which could plausibly be assumed to represent the distribution of the shortfall of output from the frontier. ALS consider (negative) half-normal and exponential distributions, while Meeusen and van den Broeck consider exponential only. Other possibilities include Gamma [Richmond (1974)] and lognormal [Greene (1980)]. ALS find very little difference in the fit of half-normal and exponential, in two empirical applications. In this paper we will restrict our attention to the half-normal case, which is the case considered in most detail by ALS.